Nonlinear vibration of stringer shell: An analytical approach

Abstract

In this study, we try to analyze the free nonlinear vibration of a stringer shell analytically. The nonlinear governing equation of the problem is derived. Homotopy perturbation method is applied completely to obtain the analytical solution of the problem. We try to provide engineers and designers to achieve the nonlinear frequency of nonlinear problems especially shell vibrations with an easy method. The effects of different parameters on the ratio of nonlinear to linear natural frequency of shells are completely studied. The homotopy perturbation method gives us an excellent agreement with numerical results for whole range of the oscillation amplitude. The first order of homotopy perturbation method leads us to highly accurate solutions as indicated in this paper.